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Full Idea
A 'partial function' is one which maps only some elements of a domain to elements in another set. For example, the reciprocal function 1/x is not defined for x=0.
Gist of Idea
A 'partial function' maps only some elements to another set
Source
Peter Smith (Intro to Gödel's Theorems [2007], 02.1 n1)
Book Ref
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.8
Related Idea
Idea 13811 A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock]
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| 21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
| 18961 | We can identify functions with certain sets - or identify sets with certain functions [Putnam] |
| 13812 | A 'zero-place' function just has a single value, so it is a name [Bostock] |
| 13811 | A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock] |
| 10074 | A 'total function' maps every element to one element in another set [Smith,P] |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| 10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
| 10209 | A function is just an arbitrary correspondence between collections [Shapiro] |
| 13700 | A 'total' function must always produce an output for a given domain [Sider] |
| 15105 | F(x) walked into a bar. The barman said.. [Sommers,W] |